First of all, it's written "better" not "hotter"...

@TMZ
Second, it's old (2009 or 2010).
Finally, when these proves aren't helping Kesha AT ALL, it doesn't mean that she lied or that Luke wasn't abusive.
Of course, they had a great realtionship at some point, they seemed VERY close. But things change fast. He was probably abusive towards her after Kesha found success.